The lesson
This lesson teaches Two-Step Inequalities. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Solve like a two-step equation
Use inverse operations to isolate the variable, just like with equations.
A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.
Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.
The one special rule
When you study the one special rule, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Solve -2x + 1 < 9.
- 1Subtract 1 from both sides: -2x < 8.
- 2Divide by -2 and flip the sign: x > -4.
Why this matters
Two-Step Inequalities shows up constantly in solve like equations - but flip the sign when you multiply or divide by a negative. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Solve like a two-step equation
- The one special rule
Video walkthrough
Multi-Step Inequalities
Solve inequalities and know when to reverse the sign.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfSolve: x − 4 > 10.
Step-by-step solution
- 1Add 4 to both sides: x > 14.
Exercise 2
Try it yourselfSolve: 3m + 6 ≤ 21.
Step-by-step solution
- 1Subtract 6: 3m ≤ 15.
- 2Divide by 3: m ≤ 5.
Exercise 3
Try it yourselfSolve: −2x + 8 ≥ 2.
Step-by-step solution
- 1Subtract 8: -2x ≥ -6.
- 2Divide by -2 and flip the sign: x ≤ 3.
Exercise 4
Try it yourselfSolve: 5 − 3y < 14.
Step-by-step solution
- 1Subtract 5: -3y < 9.
- 2Divide by -3 and flip: y > -3.
Exercise 5
Try it yourselfYou need at least $45 for a field trip. You have $18 and earn $9 per chore. How many chores c are needed?
Step-by-step solution
- 1Inequality: 18 + 9c ≥ 45.
- 2Subtract 18: 9c ≥ 27.
- 3Divide by 9: c ≥ 3.
- 4You need at least 3 chores.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Two-Step Inequalities
Question 1 of 4
Solve: 2x + 3 > 11.